Semi-Classical Analysis for Hartree Equations in Some Supercritical Cases

We study the semi-classical limit of the Hartree equation, which has focusing at a point. There exists a critical index indicating nonlinear effect around the caustic, and it is known that the influence by the nonlinearity is negligible in subcritical case (called linear caustic case), and that it is not in critical case (nonlinear caustic case). We give the asymptotic behavior beyond caustic in some supercritical cases which give rise to very strong nonlinear effect. Submitted: August 25, 2006. Accepted: December 11, 2006.     

Minimal cocycles with the scaling property and substitutions

‘Fractal’ functions are formulated as a minimal cocycle on a topological dynamics which admits nontrivial scaling transformations. In this paper, it is proved that if in addition it admits a continuous family of scaling transformations, then itscapacity is not ino(N ²). We define minimal cocycles with nontrivial scaling transformations coming from substitutions on a finite alphabet which are proved to have capacityO(N), so that they admit only a discrete family of scaling transformations. We also construct one which has capacityO(N ²) and admit a continuous family of scaling transformations. Supported by C.N.R.S.(U.R.A 225); Partially supported by the Japan Society for the Promotion of Science.     

Temperature-disturbance free magnetic field sensor based on double fiber optic polarimetry

A double fiber-optic Mach-Zehnder interferometer for sensing magnetic fields is devised using two polarization maintaining single-mode fibers. This sensor achieves not only highly sensitive performance but also excellent immunity from temperature disturbance. The sensitivity attains 243 deg/mT (mT=10^-3N/A) for the sensing part of the 5 cm long fiber.     

Synthesis of TiC-C fiber from titanium isopropoxide treated phenolic resin fiber

Precursor fibers for titanium carbide-carbon fibers were synthesized by reacting phenolic resin fibers with titanium isopropoxide (TIP). In this system, titanium oxide gel coated fiber was prepared by hydrolyzing TIP infiltrated resin fiber. The precursor fibers obtained after the hydrolysis were converted into titanium oxide-carbon fibers (TiO₂-C fibers) by pyrolysis at 1273 K. The TiO₂-C fibers were converted into titanium carbide-carbon fibers (TiC-C fibers) by heat treatment at 1373–1973 K. The mechanisms of the conversion from TiO₂-C fibers to TiC-C fibers were characterized by TGA.     

Cis and trans 4,8-dimethyl-6-phenyl-5,6,7,8-tetra-hydro-4H-1,3,6-oxadiazocin-2-ones: Conformational studies and configurational assignments by NMR

The reaction of N-(2-aminopropyl)-N-(2-hydroxypropyl)aniline with phosgene afforded cis and trans isomers of 4,8-dimethyl-6-phenyl-5,6,7,8-tetrahydro-4H-1,3,6-oxadiazocin-2-one. On the basis of ASIS data and Eu-shift difference, the title compounds are found to exist as boat-chair conformation in which the carbonyl carbon resides at the BC-2 position on the molecular plane.     

Theory of tunneling conductance of STS around magnetic impurity in superconductors

Local density of states of quasiparticles around the magnetic impurity in superconductors are calculated on the basis of a pair potential the spatial dependence of which is determined self-consistently using negative Hubbard model. The spatial dependence of the tunneling conductance observed by Scanning tunneling spectroscopy (STS) strongly depends on the magnitude of the impurity potentials.     

A Twining Character Formula For Demazure Modules

We prove a formula for the twining characters of certain Demazure modules, over a Borel subalgebra \mathfrakb\mathfrak{b} of a finite dimensional complex semisimple Lie algebra \mathfrakg\mathfrak{g}. This formula describes the twining character of the Demazure module by the w\omega-Demazure operator associated to an element of the Weyl group that is fixed by the Dynkin diagram automorphism w\omega of \mathfrakg\mathfrak{g}. Our result is a refinement of the twining character formula for the irreducible highest weight \mathfrakg\mathfrak{g}-modules of symmetric dominant integral highest weights, and also of the ordinary Demazure character formula.     

Charge transfer in duplex DNA containing mismatch

A theory for charge transfer between the electrode and the donor/acceptor molecule coupled through a DNA bridge in solution is developed. We explore the crossover between the coherent tunneling and the incoherent sequential transfer regimes by varying the electrode potential and discuss the effects of single-base mismatches in DNA duplex in both regimes. In the former regime a single-base mismatch in DNA duplex causes a reduction in the charge transfer rate simply by decreasing the electron tunneling matrix element, however, in the latter regime the effects are rather complicated.     

SnCl4-promoted rearrangement of 2,3-epoxy alcohol derivatives: stereochemical control of the reaction

The SnCl₄-promoted rearrangement of 2,2,3,3-tetrasubstituted-2,3-epoxy-1-alcohol derivatives proceeded in a regio- and stereo-controlled manner to selectively give two types of rearranged products from a single isomer by changing the protecting group of the alcohol.